>> I have done a great deal of work to understand how modern mathematical>> logic has reached the point where its foundations are almost>> exclusively focused on non-circularity. So, while you see this>> condition as a matter of fact, such a claim in the mathematics>> community may get you some metaphorical version of tar and feathers.

> My point was that mathematical logic is not logic, it's mathematics: it's an > abuse of language. Then I don't see why the mathematician should flame the > logician for a claim on logic, all the more so when the logician in question > is saying that mathematics cannot be reduced to logic in any meaningful > sense (and vice versa). In simpler terms, what I can see in the logistic > approach is, firstly reduce all endeavours to mechanics, then call > mathematics logic, finally assert that all derives from logic.

Mathematical logic is not all of logic, but it is logic, notmathematics. There is more to the logic which is used by mathematicians, such as in metamathematics, than is in thefirst order predicate calculus, which is what is used inmathematical proofs. There are metamathematical proofs ofmathematical theorems which do not have mathematical proofs.

There is also inductive logic, which is best represented bystatistical decision theory, and there are modal logics. Ihave seen description of "quantum logics", but I do not seethem as more than partial representations.

................................

> Julio

-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558